3p/(12pq+4q) รท 8p^2/(6p^2 + 2pq)
You asked:
Evaluate the expression: \(\frac{\frac{\frac{3 p}{12 p q + 4 q}}{8 \cdot {p}^{2}}}{6 \cdot {p}^{2} + 2 p q}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{\frac{\frac{3 p}{12 p q + 4 q}}{8 \cdot {p}^{2}}}{6 \cdot {p}^{2} + 2 p q} = \frac{3}{8 p \left(6 p^{2} + 2 p q\right) \left(12 p q + 4 q\right)} \)
Expanded
\[\frac{\frac{\frac{3 p}{12 p q + 4 q}}{8 \cdot {p}^{2}}}{6 \cdot {p}^{2} + 2 p q} = \frac{3 p}{576 p^{5} q + 192 p^{4} q^{2} + 192 p^{4} q + 64 p^{3} q^{2}}\]
Factored
\[\frac{\frac{\frac{3 p}{12 p q + 4 q}}{8 \cdot {p}^{2}}}{6 \cdot {p}^{2} + 2 p q} = \frac{3}{64 p^{2} q \left(3 p + 1\right) \left(3 p + q\right)}\]